The equation of the plane through (4,4,0) and perpendicular to th

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 Multiple Choice QuestionsMultiple Choice Questions

421.

A person observes the top of a tower from a point A on the ground. The elevation of the tower from this point is 60°. He moves 60 min the direction perpendicular to the line joining A and base of the tower. The angle of elevation of the tower from this point is 45°.Then, the height of the tower (in metres) is

  • 6032

  • 602

  • 6023

  • 603


422.

The direction ratios of the two lines AB and AC are 1, - 1, - 1 and 2, - 1, 1. The direction ratios of the normal to the plane ABC are

  • 2, 3, -1

  • 2, 2, 1

  • 3, 2, - 1

  • - 1, 2, 3


423.

A plane passing through(- 1, 2, 3) and whose normal makes equal angles with the coordinate axes is

  • x + y + z + 4 = 0

  • x - y + z + 4 = 0

  • x + y + z - 4 = 0

  • x + y + z = 0


424.

A variable plane passes through a fixed point (1, 2, 3). Then, the foot of the perpendicular from the origin to the plane lies on

  • a circle

  • a sphere

  • an ellipse

  • a parabola


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425.

The angle between the lines r^ = 2i^ - 3j^ + k^ + λi^ + 4j^ + 3k^ and r^ = i^ - j^ + 2k^ + μi^ + 2j^ - 3k^ is

  • π2

  • cos-1991

  • cos-1784

  • π3


426.

The locus of the centroid of the triangle with vertices at (acos(θ), asin(θ)), (bsin(θ), - bcos(θ)) and (1, 0) is (here, θ is a parameter)

  • 3x + 12 + 9y2 = a2 + b2

  • 3x - 12 + 9y2 = a2 - b2

  • 3x - 12 + 9y2 = a2 + b2

  • 3x + 12 + 9y2 = a2 - b2


427.

If (2, - 1, 2) and (K, 3, 5) are the triads of direction ratios of two lines and the angle between them is 45°, then the value of K is

  • 2

  • 3

  • 4

  • 6


428.

The length of perpendicular from the origin to the plane which makes intercepts 13, 14 and 15 respectively on the coordinate axes is

  • 152

  • 110

  • 52

  • 5


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429.

If the plane 56x + 4y + 9z = 2016 meets the coordinate axes in A, B, C, then the centroid of the ABC is

  • 12, 168, 2243

  • (12, 168, 224)

  • (12, 168, 112)

  • 12, -168, 2243


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430.

The equation of the plane through (4,4,0) and perpendicular to the planes 2x + y + 2z + 3 = 0 and 3x + 3y + 2z - 8 = 0

  • 4x + 3y + 3z = 28

  • 4x - 2y - 3z = 8

  • 4x + 2y + 3z = 24

  • 4x +2y - 3z = 24


B.

4x - 2y - 3z = 8

(b) Equations of plane passing through (4, 4, 0) is given by a(x - 4) + b(y - 4) + c(z - 0) = 0, where a, b, c are DR's of normal to the plane

Since this plane is to the given plans, therefore,

we get

2a + b + 2c =0

and 3a + 3b + 2c = 0

By cross-multiplication method

a2 - 6 =  - b4 - 6 = c6 - 3 a - 4 = b2 = c3So, the required equation of plane is-4x - 4 + 2y - 4 + 3z = 0 - 4x +16 +2y - 8 + 3z = 0 4x - 2y - 3z = 8


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